Nonlinear Vibration


Lecture 1 - Introduction of Nonlinear systems


Lecture 2 - Review of Linear vibrating systems


Lecture 3 - Phenomena associated with Nonlinear systems


Lecture 4 - Commonly observed Phenomena in Nonlinear systems


Lecture 5 - Force and Moment based Approach


Lecture 6 - Energy based approach Extended Hamilton’s principle and Lagrange Priciple


Lecture 7 - Derivation of Equation of motion of nonlinear discrete system (More examples)


Lecture 8 - Derivation of Equation of motion of nonlinear continuous system - 1


Lecture 9 - Derivation of Equation of motion of nonlinear continuous system - 2


Lecture 10 - Ordering of nonlinear Equation of motion


Lecture 11 - Qualitative Analysis Straight forward expansion


Lecture 12 - Numerical method Straight forward expansion


Lecture 13 - Lindstedt Poincare’ technique


Lecture 14 - Method of multiple scales


Lecture 15 - Method of Harmonic balance


Lecture 16 - Method of averaging


Lecture 17 - Generalized Method of averaging


Lecture 18 - Krylov-Bogoliubov-Mitropolski technique


Lecture 19 - Incremental harmonic balance method and Intrinsic multiple scale harmonic balance method


Lecture 20 - Modified Lindstedt Poincare’ technique


Lecture 21 - Stability and Bifurcation of Fixed-point response - 1


Lecture 22 - Stability and Bifurcation of Fixed-point response - 2


Lecture 23 - Stability and Bifurcation of Fixed-point response - 3


Lecture 24 - Stability and Bifurcation of Fixed-point response - 4


Lecture 25 - Stability Analysis of Periodic response


Lecture 26 - Bifurcation of Periodic response And Introduction to quasi-periodic and Chaotic response


Lecture 27 - Quasi-Periodic and Chaotic response


Lecture 28 - Numerical methods to obtain roots of characteristic equation and time response


Lecture 29 - Numerical methods to obtain time response


Lecture 30 - Numerical methods to obtain frequency response


Lecture 31 - Free Vibration of Single degree of freedom Nonlinear systems with Cubic and quadratic nonlinearities


Lecture 32 - Free Vibration of Single degree of freedom Nonlinear systems with Cubic and quadratic nonlinearities: effect of damping


Lecture 33 - Free Vibration of multi- degree of freedom Nonlinear systems with Cubic and quadratic nonlinearities


Lecture 34 - Forced nonlinear Vibration Single degree of freedom Nonlinear systems with Cubic nonlinearities:


Lecture 35 - Forced nonlinear Vibration Single and multi- degree of freedom Nonlinear systems


Lecture 36 - Nonlinear Forced-Vibration of Single and Multi Degree-of-Freedom System


Lecture 37 - Analysis of Multi- degree of freedom system


Lecture 38 - Nonlinear Vibration of Parametrically excited system: Axially loaded sandwich beam


Lecture 39 - Nonlinear Vibration of Parametrically excited system: Elastic and Magneto-elastic beam


Lecture 40 - Nonlinear Vibration of Parametrically excited system with internal resonance